Fill in the blank of the triangle below x=

ANSWER

EXPLANATION

From the given right angle triangle the known angle is 47°

The side length which is x units is opposite to the known angle.

We also know a side length 35 units which is adjacent to the given angle.

We use the tangent ratio to obtain,

x = 37.53 units

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

From the figure we can see a right angled triangle with one angle is 47° and adjacent  side length of that angle is 35

To find the value of x

From the figure we can write,

Tan 47 =  Opposite side/Adjacent side

 = x/35

x = 35 * Tan 47

 = 37.53 units

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Work Shown:

Refer to the diagram below. The short leg (opposite the 30 degree angle) is equal to 1 unit, the long leg is equal to sqrt(3) units, and the hypotenuse is 2 units long.

For the reference angle 60 degrees, the opposite leg is sqrt(3) units and the adjacent leg is 1 unit

tan(angle) = opposite/adjacent

tan(60) = sqrt(3)/1

tan(60) = sqrt(3)